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A125269
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Minimal number of states required for a 2-symbol, 5-tuple Turing machine that takes n steps on an initially blank tape before halting.
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1
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1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If BB(n) = A060843(n), then a(BB(n)) = n and that is the last occurrence of n in this sequence. a(n) will not become monotonic; if it did, we could compute BB(n), since a(n) is computable. a(n) diverges properly, but does so very slowly. The terms with values 1,2,3 were computed by exhaustive search. The terms with value 4 were inferred from knowing that they are greater than 3 and from the observation that for all n, a(n+1) <= a(n) + 1 (an easy construction). Using exhaustive search, may be able to extend the sequence to (most of) the terms up to and a bit beyond a(107) = 4, but going much further would likely require a more sophisticated method (see A052200).
If BB(n) = A060843(n), then a(BB(n)) = n and that is the last occurrence of n in this sequence. a(n) will not become monotonic; if it did, we could compute BB(n), since a(n) is computable. a(n) diverges properly, but does so very slowly. a(n+1) <= a(n) + 1 (an easy construction). - Martin Fuller (martin_n_fuller(AT)btinternet.com), Feb 14 2007
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LINKS
| Martin Fuller, Table of n, a(n) for n = 1..626
Martin Fuller, Illustration file listing a Turing machine for each n
H. Marxen, Info on the Busy Beaver problem
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CROSSREFS
| Cf. A060843, A052200.
Sequence in context: A064876 A105517 A056813 * A077430 A105513 A004233
Adjacent sequences: A125266 A125267 A125268 * A125270 A125271 A125272
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KEYWORD
| nice,nonn
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AUTHOR
| Dustin Wehr (robert.wehr(AT)mail.mcgill.ca), Jan 16 2007, Jan 28 2007
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EXTENSIONS
| More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Feb 14 2007
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